# NonLinModelling: Chaotic Time Series Modelling In fNonlinear: Rmetrics - Nonlinear and Chaotic Time Series Modelling

## Description

A collection and description of functions to simulate different types of chaotic time series maps.

Chaotic Time Series Maps:

 `tentSim` Simulates data from the Tent Map, `henonSim` simulates data from the Henon Map, `ikedaSim` simulates data from the Ikeda Map, `logisticSim` simulates data from the Logistic Map, `lorentzSim` simulates data from the Lorentz Map, `roesslerSim` simulates data from the Roessler Map.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```tentSim(n = 1000, n.skip = 100, parms = c(a = 2), start = runif(1), doplot = FALSE) henonSim(n = 1000, n.skip = 100, parms = c(a = 1.4, b = 0.3), start = runif(2), doplot = FALSE) ikedaSim(n = 1000, n.skip = 100, parms = c(a = 0.4, b = 6.0, c = 0.9), start = runif(2), doplot = FALSE) logisticSim(n = 1000, n.skip = 100, parms = c(r = 4), start = runif(1), doplot = FALSE) lorentzSim(times = seq(0, 40, by = 0.01), parms = c(sigma = 16, r = 45.92, b = 4), start = c(-14, -13, 47), doplot = TRUE, ...) roesslerSim(times = seq(0, 100, by = 0.01), parms = c(a = 0.2, b = 0.2, c = 8.0), start = c(-1.894, -9.920, 0.0250), doplot = TRUE, ...) ```

## Arguments

 `doplot` a logical flag. Should a plot be displayed? `n, n.skip` [henonSim][ikedaSim][logisticSim] - the number of chaotic time series points to be generated and the number of initial values to be skipped from the series. `parms` the named parameter vector characterizing the chaotic map. `start` the vector of start values to initiate the chaotic map. `times` [lorentzSim][roesslerSim] - the sequence of time series points at which to generate the map. `...` arguments to be passed.

## Value

[*Sim] -
All functions return invisible a vector of time series data.

## Author(s)

Diethelm Wuertz for the Rmetrics R-port.

## References

Brock, W.A., Dechert W.D., Sheinkman J.A. (1987); A Test of Independence Based on the Correlation Dimension, SSRI no. 8702, Department of Economics, University of Wisconsin, Madison.

Eckmann J.P., Oliffson Kamphorst S., Ruelle D. (1987), Recurrence plots of dynamical systems, Europhys. Letters 4, 973.

Hegger R., Kantz H., Schreiber T. (1999); Practical implementation of nonlinear time series methods: The TISEAN package, CHAOS 9, 413–435.

Kennel M.B., Brown R., Abarbanel H.D.I. (1992); Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A45, 3403.

Rosenstein M.T., Collins J.J., De Luca C.J. (1993); A practical method for calculating largest Lyapunov exponents from small data sets, Physica D 65, 117.

`RandomInnovations`.

## Examples

 ```1 2 3 4``` ```## logisticSim - set.seed(4711) x = logisticSim(n = 100) plot(x, main = "Logistic Map") ```

### Example output

```Loading required package: timeDate

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